a. Field of invention
The invention relates to aircraft control systems and, more particularly, to a system and method for extremum-seeking-control for formation flight using blended and weighted performance parameters to optimize the conglomerate drag reduction function.
b. Background of the invention
Formation-flight-for-drag-reduction provides significant fuel savings for a formation of aircraft, and is an active area of research. See, e.g., M. Beukenberg and D. Hummel, “Aerodynamics, performance and control of air-planes in formation flight,” in Proceedings of the 17th Congress of the International Council of the Aeronautical Sciences. ICAS-90-5.9.3, September 9-14 1990; S. A. Ning, T. C. Flanzer, and I. M. Kroo, “Aerodynamic performance of extended formation flight,” in 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA, Orlando, Fla.: AIAA, January 2010; G. C. Bower, T. C. Flanzer, and I. M. Kroo, “Formation geometries and route optimization for commercial formation flight,” in 27th AIAA Applied Aerodynamics Conference, San Antonio, Tex., June 2009; M. J. Vachon, R. J. Ray, K. R. Walsh, and K. Ennix, “F\A-18 aircraft performance benefits measured during the autonomous formation flight project,” AIAA Guidance, Navigation and Control Conference, 2002.
In a formation of two aircraft, the trailing aircraft is positioned such that its wing span resides in the up-wash created by the wake vortices of the leading aircraft. This is typically realized with the trailing aircraft's wing-tip residing near the core of the leading aircraft's inboard wake vortex. Due to the asymmetric nature of the wake vortex, asymmetric aerodynamic forces act on the trailing aircraft. These forces result in effects such as an induced rolling moment, pitching moment, and yawing moment on the trailing aircraft. Effects on the leading aircraft are typically negligible. The strength of these effects depends upon the relative position of the aircraft in the formation.
Some drag reduction solutions submit a priori information about time-varying parameters to a software model, but these cannot work in applications where a priori information does not exist or is not timely available. Under such circumstances, a non-model-based “extremum seeking” or “peak-seeking” control schema is a more practical approach. Peak-seeking controllers use measurements of input and output signals and dynamically maximize or minimize a function, and do not require a priori model. Peak-seeking control is very accurate because it uses the current flight data to find the optimum, and not just theoretical or empirical models with uncertainties. Examples of automatic control systems intended to realize formation-flight-for-drag-reduction that employ an extremum seeking control system to optimize the drag reduction benefits include: J. J. Ryan and J. L. Speyer, “Peak-Seeking Control Using Gradient And Hessian Estimates,” in Proceedings of the American Control Conference, Baltimore, Md.: ACC, June 2010, pp. 611-616; D. Chichka, J. Speyer, C. Fanti, and C. Park, “Peak-Seeking Control For Drag Reduction In Formation Flight,” J. Guid. Control Dyn., vol. 29, no. 5, pp. 1221-1230, September-October 2006; and P. Binetti, K. B. Ariyur, M. Krstic; F. Bernelli, “Formation flight optimization using extremum seeking feedback,” Journal Of Guidance, Control, And Dynamics, vol. 26, pp. 132-142, 2003; and E. Lavretsky, N. Hovakimyan, A. Calise, and V. Stepanyan, “Adaptive Vortex Seeking Formation Flight Neurocontrol,” in in AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, Tex., 2003, pp. 11-14. Each of these systems estimates the local gradient of a performance function and commands the trailing aircraft of the formation to a relative position which minimizes the gradient of the performance function.
Ideally, such a formation flight control system would employ a performance function formed from measurements of drag-reduction thereby directly maximizing the drag reduction achieved during flight. Unfortunately drag-reduction is not directly measurable and difficult to estimate. Conventional approaches side-step this issue by extremizing performance functions formed from measurements analogous to drag-reduction. For example Lavretsky et al. minimize throttle activity, Chichka et al. maximizes the induced rolling moment, and Binetti et al. maximizes the induced pitch angle. With each of these approaches, the extremum seeking control system improves the drag reduction achieved; however, the true drag reduction extremum coordinates do not necessarily coincide with that of the analogous measurement.
What is needed is an extremum-seeking control system for formation flight that uses blended performance parameters in a conglomerate performance function that better approximates drag reduction than performance functions formed from individual measurements.